Use our free GCF of Fractions Calculator tool to compute the GCF of 35/69, 266/78, 658/649 i.e 7/1164306 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/69, 266/78, 658/649.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/69,266/78,658/649
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 35/69,266/78,658/649, numerators are 35,266,658
Denominators are 69,78,649
The GCF of 35,266,658 is 7 .
LCM of 69,78,649 is 1164306.
The greatest common factor of 35/69,266/78,658/649 = [GCF of 35,266,658]/[LCM of 69,78,649]= 7/1164306
Therefore, the GCF of 35/69,266/78,658/649 is 7/1164306.
To find the highest common factor of 35,266,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 35,266,658 is 7.
Lets's calculate GCF of 35,266,658
7 | 35, 266, 658 |
5, 38, 94 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 35,266,658 . The biggest common factor number is the GCF number.
So the greatest common factor 35,266,658 is 7.
Lets's calculate LCM of 69,78,649
3 | 69, 78, 649 |
23, 26, 649 |
∴ So the LCM of the given numbers is 3 x 23 x 26 x 649 = 1164306
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/1164306
Therefore, the GCF of Fractions 35/69,266/78,658/649 is 7/1164306
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 69,78,649 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,78,649) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(69,78,649) x common factors =1 x 3 = 3
LCM(69,78,649) = ( 69 × 78 × 649 ) / 3
LCM(69,78,649) = 3492918 / 3
LCM(69,78,649) = 1164306
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,266,658?
The HCF of 35,266,658 is 7
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 35/69, 266/78, 658/649?
Answer: GCF of Numerators as per given numbers 35/69, 266/78, 658/649 is
GCF of Numerators i.e. for 35,266,658 is 7
LCM of denominators i.e. for 69,78,649 is 1164306.
Thus, GCF of Fractions is 7/1164306.Finally, GCF of Fractions for 35/69, 266/78, 658/649 is 7/1164306.